On pre-Novikov algebras and derived Zinbiel variety

For a non-associative algebra $A$ with a derivation $d$, its derived algebra $A^{(d)}$ is the same space equipped with new operations $a\succ b = d(a)b$, $a\prec b = ad(b)$, $a,b\in A$. Given a variety Var of algebras, its derived variety is generated by all derived algebras $A^{(d)}$ for all $A$ in Var and for all derivations $d$ of $A$. The same terminology is applied to binary operads governing varieties of non-associative algebras. For example, the operad of Novikov algebras is the derived one for the operad of (associative) commutative algebras. We state a sufficient condition for every algebra from a derived variety to be embeddable into an appropriate differential algebra of the corresponding variety. We also find that for the variety Zinb of Zinbiel algebras, there exist algebras from the derived variety (which coincides with the class of pre-Novikov algebras) that cannot be embedded into a Zinbiel algebra with a derivation.Comment: 14 pages, minor revisio

Singlet-Triplet Excitations in the Unconventional Spin-Peierls System TiOBr

We have performed time-of-flight neutron scattering measurements on powder samples of the unconventional spin-Peierls compound TiOBr using the fine-resolution Fermi chopper spectrometer (SEQUOIA) at the SNS. These measurements reveal two branches of magnetic excitations within the commensurate and incommensurate spin-Peierls phases, which we associate with n = 1 and n = 2 triplet excitations out of the singlet ground state. These measurements represent the first direct measure of the singlet-triplet energy gap in TiOBr, which is determined to be Eg = 21.2 +/- 1.0 meV.Comment: 5 pages, 4 figures, submitted for publicatio

Kondo behavior, ferromagnetic correlations, and crystal fields in the heavy Fermion compounds Ce3X (X=In, Sn)

We report measurements of inelastic neutron scattering, magnetic susceptibility, magnetization, and the magnetic field dependence of the specific heat for the heavy Fermion compounds Ce$_3$In and Ce$_3$Sn. The neutron scattering results show that the excited crystal field levels have energies $E_1$ = 13.2 meV, $E_2$ = 44.8 meV for Ce$_3$In and $E_1$ = 18.5 meV, $E_2$ = 36.1 meV for Ce$_3$Sn. The Kondo temperature deduced from the quasielastic linewidth is 17 K for Ce$_3$In and 40 K for Ce$_3$Sn. The low temperature behavior of the specific heat, magnetization, and susceptibility can not be well-described by J=1/2 Kondo physics alone, but require calculations that include contributions from the Kondo effect, broadened crystal fields, and ferromagnetic correlations, all of which are known to be important in these compounds. We find that in Ce$_3$In the ferromagnetic fluctuation makes a 10-15 % contribution to the ground state doublet entropy and magnetization. The large specific heat coefficient $\gamma$ in this heavy fermion system thus arises more from the ferromagnetic correlations than from the Kondo behavior.Comment: 8 pages, 6 figure

Neutron scattering and scaling behavior in URu2Zn20 and YbFe2Zn20

The dynamic susceptibility chi"(deltaE), measured by inelastic neutron scattering measurements, shows a broad peak centered at Emax = 16.5 meV for the cubic actinide compound URu2Zn20 and 7 meV at the (1/2, 1/2, 1/2) zone boundary for the rare earth counterpart compound YbFe2Zn20. For URu2Zn20, the low temperature susceptibility and magnetic specific heat coefficient gamma = Cmag/T take the values chi = 0.011 emu/mole and gamma = 190 mJ/mole-K2 at T = 2 K. These values are roughly three times smaller, and Emax is three times larger, than recently reported for the related compound UCo2Zn20, so that chi and gamma scale inversely with the characteristic energy for spin fluctuations, Tsf = Emax/kB. While chi(T), Cmag(T), and Emax of the 4f compound YbFe2Zn20 are very well described by the Kondo impurity model, we show that the model works poorly for URu2Zn20 and UCo2Zn20, suggesting that the scaling behavior of the actinide compounds arises from spin fluctuations of itinerant 5f electrons.Comment: 7 pages, 5 figure

Eigenvalue correlations in non-Hermitean symplectic random matrices

Correlation function of complex eigenvalues of N by N random matrices drawn from non-Hermitean random matrix ensemble of symplectic symmetry is given in terms of a quaternion determinant. Spectral properties of Gaussian ensembles are studied in detail in the regimes of weak and strong non-Hermiticity.Comment: 14 page